Preheat the oven to 375 degrees F. Thoroughly butter and flour the madeleine pans.

In the bowl of an electric mixer fitted with the paddle attachment, beat the eggs, sugar, and vanilla on medium speed for 3 minutes, or until light yellow and fluffy. Add 1/4 pound of butter and mix. Sift together the flour, cornstarch, baking powder, and salt, and stir into the batter with a rubber spatula. Stir in the coconut.

With a soup spoon, drop the batter into the pans, filling each shell almost full. Bake the madeleines for 10 to 12 minutes, until they spring back when pressed. Tap the madeleines out onto a baking pan lined with parchment paper and allow to cool. Dust with confectioners' sugar, if desired.